We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field—assumed to be the real or the complex numbers—and which contains the field. Notably, we consider Fueter expansions, Gleason’s problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and related problems. Such a framework includes many familiar algebras as particular cases. The quaternions, the split quaternions, the Clifford algebras, the ternary algebra, and the Grassmann algebra are a few examples of them.

中文翻译：

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Fueter 变量函数的一般设置：可微性、有理函数、Fock 模块和相关主题

我们发展了超全纯函数理论的某些方面，其值取自一个域上的 Banach 代数——假设是实数或复数——并且包含该域。值得注意的是，我们考虑了 Fueter 展开、Gleason 问题、超全纯有理函数理论、Fueter 级数的模块和相关问题。这样的框架包括许多熟悉的代数作为特殊情况。四元数、分裂四元数、克利福德代数、三元代数和格拉斯曼代数就是其中的几个例子。